# A two weight weak inequality for potential type operators

Vachtang Michailovič Kokilashvili; Jiří Rákosník

Commentationes Mathematicae Universitatis Carolinae (1991)

- Volume: 32, Issue: 2, page 251-263
- ISSN: 0010-2628

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topKokilashvili, Vachtang Michailovič, and Rákosník, Jiří. "A two weight weak inequality for potential type operators." Commentationes Mathematicae Universitatis Carolinae 32.2 (1991): 251-263. <http://eudml.org/doc/247285>.

@article{Kokilashvili1991,

abstract = {We give conditions on pairs of weights which are necessary and sufficient for the operator $T(f)=K\ast f$ to be a weak type mapping of one weighted Lorentz space in another one. The kernel $K$ is an anisotropic radial decreasing function.},

author = {Kokilashvili, Vachtang Michailovič, Rákosník, Jiří},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {integral operator; anisotropic potential; weighted Lorentz space; weak type inequalities; two weight functions; potential operators; Lorentz spaces; metric},

language = {eng},

number = {2},

pages = {251-263},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {A two weight weak inequality for potential type operators},

url = {http://eudml.org/doc/247285},

volume = {32},

year = {1991},

}

TY - JOUR

AU - Kokilashvili, Vachtang Michailovič

AU - Rákosník, Jiří

TI - A two weight weak inequality for potential type operators

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1991

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 32

IS - 2

SP - 251

EP - 263

AB - We give conditions on pairs of weights which are necessary and sufficient for the operator $T(f)=K\ast f$ to be a weak type mapping of one weighted Lorentz space in another one. The kernel $K$ is an anisotropic radial decreasing function.

LA - eng

KW - integral operator; anisotropic potential; weighted Lorentz space; weak type inequalities; two weight functions; potential operators; Lorentz spaces; metric

UR - http://eudml.org/doc/247285

ER -

## References

top- Chang H.M., Hunt R.A., Kurtz D.S., The Hardy-Littlewood maximal function on $L(p,q)$ spaces with weight, Indiana Univ. Math. J. 31 (1982), no.1, 109-120. (1982) MR0642621
- Gabidzashvili M., Weighted inequalities for anisotropic potentials, Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 82 (1986), 25-36. (1986) MR0884696
- Gabidzashvili M., Genebashvili J., Kokilashvili V., Two weight inequalities for generalized potentials (in Russian), Trudy Mat. Inst. Steklov, to appear. MR1221297
- Kokilashvili V., Weighted inequalities for maximal functions and fractional integrals in Lorentz spaces, Math. Nachr. 133 (1987), 33-42. (1987) Zbl0652.42005MR0912418
- Kokilashvili V., Gabidzashvili M., Weighted inequalities for anisotropic potentials and maximal functions (in Russian), Dokl. Akad. Nauk SSSR 282 (1985), no. 6, 1304-1306 English translation: Soviet Math. Dokl. 31 (1985), no. 3, 583-585. (1985) MR0802694
- Kokilashvili V., Gabidzashvili M., Two weight weak type inequalities for fractional type integrals, preprint no. 45, Mathematical Institute of the Czechoslovak Academy of Sciences, Prague 1989.
- Sawyer E.T., A two weight type inequality for fractional integrals, Trans. Amer. Math. Soc. 281 (1984), no. 1, 339-345. (1984) MR0719674

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